def test_minimum_bkwd(x, data):
""" index conforms strictly to basic indexing """
y = data.draw(hnp.arrays(shape=broadcastable_shape(x.shape, max_dim=5),
dtype=float,
elements=st.floats(-10., 10.)),
label="y")
assume(not np.any(np.isclose(x, y)))
x_arr = Tensor(np.copy(x))
y_arr = Tensor(np.copy(y))
o = minimum(x_arr, y_arr)
grad = data.draw(hnp.arrays(shape=o.shape,
dtype=float,
elements=st.floats(1, 10),
unique=True),
label="grad")
(o * grad).sum().backward()
dx, dy = numerical_gradient_full(np.minimum,
x,
y,
back_grad=grad,
as_decimal=True)
assert_allclose(x_arr.grad, dx)
assert_allclose(y_arr.grad, dy)
def test_minimum_bkwd_equal():
""" regression test for documented behavior of minimum/minimum where
x == y"""
x = Tensor([1.0, 0.0, 2.0])
y = Tensor([2.0, 0.0, 1.0])
o = minimum(x, y)
o.backward()
assert_allclose(x.grad, [1.0, 0.0, 0.0])
assert_allclose(y.grad, [0.0, 0.0, 1.0])
o.null_gradients()
def leaky_relu(x, slope, constant=False):
""" Returns the leaky rectified linear activation elementwise along x.
The leaky ReLU is given by `max(x, 0) + slope*min(x, 0)`.
Parameters
----------
x : mygrad.Tensor
Input data.
slope : Union[Real, mygrad.Tensor]
The slope of the negative activation.
constant : boolean, optional (default=False)
If ``True``, the returned tensor is a constant (it
does not back-propagate a gradient).
Returns
-------
mygrad.Tensor
The result of apply the "leaky relu" function elementwise to `x`.
Examples
--------
>>> import mygrad as mg
>>> from mygrad.nnet.activations import leaky_relu
>>> x = mg.arange(-5, 6)
>>> x
Tensor([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5])
>>> y = leaky_relu(x, slope=0.1); y
>>> Tensor([-0.5, -0.4, -0.3, -0.2, -0.1, 0. , 1. , 2. , 3. , 4. , 5. ])
>>> y.backward()
>>> x.grad
array([0.1, 0.1, 0.1, 0.1, 0.1, 0. , 1. , 1. , 1. , 1. , 1. ])
"""
if isinstance(slope, (ndarray, Tensor)):
slope = slope.item()
if not isinstance(slope, Real):
raise TypeError(
f"`slope` must be a real-valued scalar, got {slope} (type { type(slope)})"
)
return maximum(
x, 0, constant=constant) + slope * minimum(x, 0, constant=constant)
def leaky_relu(x, slope):
''' Returns the leaky rectified linear activation elementwise along x. The leaky ReLU is given
by max(x, 0) + slope*min(x, 0).
Parameters
----------
x : mygrad.Tensor
Input data.
slope : Union[Real, mygrad.Tensor]
The slope of the negative activation.
Returns
-------
mygrad.Tensor
The rectified `x` (elementwise max(x, 0)).
'''
return maximum(x, 0) + slope * minimum(x, 0)
def hard_tanh(x, *, lower_bound=-1, upper_bound=1):
''' Returns the hard hypterbolic tangent function.
The hard_tanh function is `lower_bound` where `x` <= `lower_bound`, `upper_bound` where
`x` >= `upper_bound`, and `x` where `lower_bound` < `x` < `upper_bound`.
Parameters
----------
x : Union[numpy.ndarray, mygrad.Tensor]
The input, to which to apply the hard tanh function.
lower_bound : Real, optional (default=-1)
The lower bound on the hard tanh.
upper_bound : Real, optional (default=1)
The upper bound on the hard tanh.
Returns
-------
mygrad.Tensor
The result of applpying the hard tanh function elementwise to `x`.
'''
return maximum(lower_bound, minimum(x, upper_bound))